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I am amazed at seeing that the limit is defined by continuity. It is interesting.
by eccstartup 11y ago
I am amazed at seeing that the limit is defined by continuity. It is interesting.
- bumbledraven 11y ago99. Expository notes Common practice in calculus books is to define continuity using limits. I define limits using continuity; continuity is a simpler concept.
- eccstartup 11y agoAre they equivalent? Or both systems work smoothly?
- dirkt 11y agoContinuity in the topological sense implies continuity by limits. For topological spaces with a countable (local) basis, the converse is also true. So, in general it's not equivalent. For the reals etc., it is.
- cottonseed 11y agoThey are equivalent if you consider limits of nets rather than limits of sequences.
- bumbledraven 11y agoThey are logically equivalent for the reals. Search the web for [limits "in terms of continuity"].